Problem: Multiply the following complex numbers, marked as blue dots on the graph: $( e^{13\pi i / 12}) \cdot (5 e^{3\pi i / 4})$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $ e^{13\pi i / 12}$ ) has angle $\frac{13}{12}\pi$ and radius $1$ The second number ( $5 e^{3\pi i / 4}$ ) has angle $\frac{3}{4}\pi$ and radius $5$ The radius of the result will be $1 \cdot 5$ , which is $5$ The angle of the result is $\frac{13}{12}\pi + \frac{3}{4}\pi = \frac{11}{6}\pi$ The radius of the result is $5$ and the angle of the result is $\frac{11}{6}\pi$.